Applying R1831: Real arithmetic expression for binomial coefficient, one has \begin{equation} \begin{split} \binom{n}{n - m} = \frac{n!}{(n - (n - m))! (n - m)!} & = \frac{n!}{m! (n - m)!} \\ & = \frac{n!}{(n - m)! m!} \\ & = \binom{n}{m} \end{split} \end{equation} $\square$